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Global calibrations for the non-homogeneous Mumford-Shah functional | Massimiliano Morini
; | Date: |
17 May 2001 | Subject: | Functional Analysis MSC-class: 49K10, 49Q20 | math.FA | Abstract: | Using a calibration method we prove that, if $Gammasubset Omega$ is a closed regular hypersurface and if the function $g$ is discontinuous along $Gamma$ and regular outside, then the function $u_{eta}$ which solves $$ egin{cases} Delta u_{eta}=eta(u_{eta}-g)& ext{in $OmegasetminusGamma$} partial_{
u} u_{eta}=0 & ext{on $partialOmegacupGamma$} end{cases} $$ is in turn discontinuous along $Gamma$ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional $$ int_{Omegasetminus S_u}|
abla u|^2 dx +{cal H}^{n-1}(S_u)+etaint_{Omegasetminus S_u}(u-g)^2 dx, $$ over $SBV(Omega)$, for $eta$ large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown. | Source: | arXiv, math.FA/0105141 | Services: | Forum | Review | PDF | Favorites |
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